no. 5
Hierarchical multilevel optimization with multiple-leaders multiple-followers setting and nonseparable objectives
RAIRO. Operations Research, Tome 55 (2021) no. 5, pp. 2915-2939

Hierarchical multilevel multi-leader multi-follower problems are non-cooperative decision problems in which multiple decision-makers of equal status in the upper-level and multiple decision-makers of equal status are involved at each of the lower-levels of the hierarchy. Much of solution methods proposed so far on the topic are either model specific which may work only for a particular sub-class of problems or are based on some strong assumptions and only for two level cases. In this paper, we have considered hierarchical multilevel multi-leader multi-follower problems in which the objective functions contain separable and non-separable terms (but the non-separable terms can be written as a factor of two functions, a function which depends on other level decision variables and a function which is common to all objectives across the same level) and shared constraint. We have proposed a solution algorithm to such problems by equivalent reformulation as a hierarchical multilevel problem involving single decision maker at all levels of the hierarchy. Then, we applied a multi-parametric algorithm to solve the resulting single leader single followers problem.

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Accepté le :
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Publié le :
DOI : 10.1051/ro/2021146
Classification : 91A65, 91A06, 91A10, 90C26
Keywords: Hierarchical game, multi-leader multi-follower, Stackelberg game, Nash game, equivalent reformulation, multi-parametric algorithm 
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     title = {Hierarchical multilevel optimization with multiple-leaders multiple-followers setting and nonseparable objectives},
     journal = {RAIRO. Operations Research},
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     publisher = {EDP-Sciences},
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Zewde, Addis Belete; Kassa, Semu Mitiku. Hierarchical multilevel optimization with multiple-leaders multiple-followers setting and nonseparable objectives. RAIRO. Operations Research, Tome 55 (2021) no. 5, pp. 2915-2939. doi: 10.1051/ro/2021146

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